Question: Simplify the following expression: $ n = \dfrac{5z + 6}{-3} - \dfrac{1}{9} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{5z + 6}{-3} \times \dfrac{9}{9} = \dfrac{45z + 54}{-27} $ Multiply the second expression by $\dfrac{-3}{-3}$ $ \dfrac{1}{9} \times \dfrac{-3}{-3} = \dfrac{-3}{-27} $ Therefore $ n = \dfrac{45z + 54}{-27} - \dfrac{-3}{-27} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{45z + 54 + 3 }{-27} $ Distribute the negative sign: $n = \dfrac{45z + 54 + 3}{-27}$ $n = \dfrac{45z + 57}{-27}$ Simplify the expression by dividing the numerator and denominator by -3: $n = \dfrac{-15z - 19}{9}$